I haven't worked with Typescript much at all but a quick google search gave me this as a first result. jonnyreeves.co.uk/2015/hello-typescript-and-mocha
It looks like, in that example, he is throwing the tests through the typescript compiler, which will import the .ts file that he wants to test And compile that along with the test file itself. He is doing the compilation before running mocha using the npm script "pre" hook.
I don't know if mocha has an actual plugin for typescript though. Worth looking for.